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When writing the equation of the line, it should be in slope intercept form:
y=mx+b |
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Quad II-----------------Quad I
Quad III---------------------Quad IV |
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If given two points in a problem, use slope formula to find m.
m=y2-y1
x2-x1
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| If a graph has an increasing slope, its slope is positive. |
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| If a graph has a decreasing slope, its a negative slope. |
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| If a graph is constant, its slope is 0. |
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| What if two lines are parallel? Then they have the same slope. |
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| If two lines are perpindicular, their slopes are opposite reciprocals. i.e. 3 and -1/3 |
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Transformation:
If your parent function is x2 then transformed it looks like this:
a) x2 +2 = up 2 units
b) x2 -2 = down 2 units
c) (x-2)2 = right 2 units
d) (x+2)2 = left 2 units |
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Transformation:
If it looks like f(x)= -x2
then it has been reflected over the x-axis |
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Axis of symmetry is simply a vertical line given by:
x=-b/2a |
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To find the vertex, you use the same formula!
(-b/2a, PLUG IT IN)
So find the vertex, and whatever you get for the vertex, plug that back into the original equation, and that will give you your y-value. |
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| Domain: the "shadow" on the X axis |
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| Range: "shadow" on the Y axis |
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| Power functions look like: xn |
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Which is the leading coefficient?
f(x)= -x3+4x
the leading coefficient is 1. |
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What is the degree?
f(x)= -x3+4x
Degree is 3. |
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If it says "Sketch the line graph thru (3,2), m=4/3"
Then you plot a point at (3,2), and then for the slope, rise 4 and run 3.
REMEMBER: rise over run (y over x) |
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If it says "state the intervals where f increases, decreases, or constant"
They are ALL OPEN INTERVALS, with ROUND PARENTHESES. |
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If it says find the linear function,
it really means write the equation of the line. |
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| To find the zeroes of a function, replace f(x) with 0. |
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| To determine if a point lies on the graph, plug the x coordinate into the equation. If it then equals the y coordinate, the point does lie on the graph. |
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if given a point and the slope, use point slope formula!
y-y1=m(x-x1) |
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Slope of horizontal line (meaning left to right) is 0.
Its equations looks like y=# |
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| Slope of vertical line (meaning up and down) is undefined. It's equation looks like x=# |
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In quadratics....
a>1 means it will be narrower than the parent function
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In quadratics....
a<1 means it will be wider than the parent function |
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How do I know the maximum number of turning points?
The degree tells you! |
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| If the leading coefficient is negative, its end behavior will fall on the right side. |
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| If the leading coefficient is positive, then its end behavior rises at the right hand side. |
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| if the degree is even, then the end behavior falls on the left side. |
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| if the degree is odd, then the end behavior rises on the left side. |
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| Even multiplicity touches the x-axis. |
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| odd multiplicity crosses the x axis. |
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| a vertex can be a maximum or a minumum. |
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| vertex is a maximum if a<0. its negative. |
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| vertex is a maximum if a>0. its positive. |
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Quadratic form:
y=ax2+bx+c |
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In quadratics...
the parabola will be concave up if a is positive |
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in quadratics...
the parabola will be concave down if a is negative |
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when given a quadratic problem, there are 4 steps to solve it:
a) is it concave up or down
b) axis of symmetry
c) find the vertex
d) find the zeroes |
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find the equation of the line:
(4,2) (4,-1)
when you find m, you get -3/0. this is undefined, meaning its a vertical line. so its equation is x=4. |
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find the equation of the line:
(2,3)(-1,3)
when you find m, you get 0/-3. this is a horizontal line. so the equation is y=3. |
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| if given a point and an equation and told to fine the parallel line, we know the slope is the same. so use the same slope, then plug in x and y to find b. then after finding b, put it all into y=mx+b form! |
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| if it says to find the equation of the line that is perpindicular, take the slope from the original equation and take the opposite reciprocal of it. then, plug in x and y into the equation to find b. after finding b, plug it and the slope back into slope intercept form to get your answer. |
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Parent function: reciprocal.
f(x)= 1/x |
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Parent function:Quadratic
f(x)= x2 |
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parent function: square foot
f(x)= √x |
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parent function: absolute value
f(x)=lxl |
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parent function: identity
f(x)=x |
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parent function: constant
f(x)= c |
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parent function: cubic
f(x)= x3 |
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